A244854 Decimal expansion of Pi^2/32.

3, 0, 8, 4, 2, 5, 1, 3, 7, 5, 3, 4, 0, 4, 2, 4, 5, 6, 8, 3, 8, 5, 7, 7, 8, 4, 3, 7, 4, 6, 1, 2, 9, 7, 2, 2, 9, 7, 8, 5, 5, 3, 1, 0, 6, 4, 7, 6, 2, 7, 4, 7, 0, 7, 0, 7, 5, 4, 1, 7, 1, 6, 8, 0, 0, 6, 8, 7, 6, 4, 0, 0, 7, 0, 0, 6, 0, 0, 1, 6, 3, 8, 4, 3, 8, 0, 5

Offset: 0

Author

Charles R Greathouse IV, Jul 07 2014

Keywords

• nonn
• cons

Comments

Probability that a point selected uniformly at random from the unit 4-cube is in the unit 4-sphere.

Let S(n) = 1 - 1/3 + 1/5 - ... + ((-1)^(n-1))/(2n-1). Then Sum{n >=1} ((-1)^(n-1))*S(n) /(2n+1) = Pi^2 /32. The convergence is very slow. - Michel Lagneau, Feb 27 2015

Examples

			Choose -1 <= w, x, y, z <= 1 uniformly at random. Then this constant is the probability that w^2 + x^2 + y^2 + z^2 <= 1.
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A003881 (2-dimensional analog), A019673 (3-dimensional analog).

Programs

Maple

Digits:=100; evalf(Pi^2/32); # Wesley Ivan Hurt, Feb 27 2015

Mathematica

RealDigits[Pi^2/32,10,120][[1]] (* Harvey P. Dale, Jul 13 2014 *)

PARI

Pi^2/32

Formula

Equals Integral_{0..infinity} x^2*BesselK(0, x)^2 dx. - Jean-François Alcover, Apr 15 2015

Equals Integral_{x=0..1} arctan(x)/(1+x^2) dx. - Amiram Eldar, Aug 09 2020

Equals Integral_{x=0..1} Integral_{y=0..1} Integral_{z=0..1} (1 + x^2 + y^2 + z^2)^(-2). - Peter Luschny, Dec 10 2022